Is that really the case? If the police is executing an illegal warrant, but comes across someone, say, murdering someone else, is that not considered evidence?
(This might very well be the case, considering the "Fruit of the Poisonous tree" doctrine).
It is, but there's a loophole: the prosecution can argue that the police inevitably would have discovered the evidence eventually. It's fairly easy to claim for something like a murder because hiding a body permanently tends to be fairly difficult, and arguing that the murderer would have successfully hidden the body is very close to an admission of guilt.
Edit: if the police interrupt and prevent a murder, the testimony of the murder victim is also admissible. I don't think the argument "if the police hadn't illegally searched the area, the victim would be dead and unable to testify" works.
(This might very well be the case, considering the "Fruit of the Poisonous tree" doctrine).